How do I create a nice miter joint between these two pieces?
As always, I'm open to correction, but creating miters at the ends of existing meshes is a fuss in Blender, unless the angle is at 45 degrees, and you can KC cut through with constraints, or ShiftCtrlAltS shear the ends of the stock pieces to a known extent. The shipped 'TinyCad' add-on can help, generating vertices at the intersections of edges, but even then, you'll find yourself creating guides of one sort or another to snap to, removing and creating faces by hand.

By far the quickest way to create miters is with polygonal curves. Create a track and a profile curve (possibly by AltC converting them from duplicated edges borrowed from existing meshes) 


The profile curve will be swept along its local Z
Its origin will lie on the track curve
Set the track curve to 2D in its data tab, fill 'None'
Set the Bevel Object of the track curve to the profile curve..




...and miters will be formed at every corner. The rightmost object has beeen converted back to a mesh; you may have to hit CtrlN in Edit mode to make its normals consistent.